I don't think it affects the Sky brand more than drink driving. He's an idiot, but in the general scheme of things, it's a fairly minor offence. A suspension and then move on.
It does, because it's football related. If he got into a fracas over nothing in a pub or whatever, then it's aside from Sky (even though he arguably still has a public profile to maintain).
He's on Sky as the face of football punditry, to argue, debate and give an impartial viewpoint over football. He adds a bit of current social trend I guess with his banter to his ex-peers (Neville, Henry, etc), but that's where the dangerous grey area is, because it continues and exaggerates this perceived "us and them" mentality, which is fine in the context of the game and for the sheer entertainment value and good old fashioned banter, but this incident is an extension of that and it's overstepped the mark.
I can't see how it's not easily related to his job. So if he'd given it out on TV all afternoon to Gary Neville, taunting Mancs in the process, and then this happened what would the reaction be then? It would be exactly the same, because it's a continuation of the same stuff. As someone said earlier, he's always giving it out on Twitter, goading other players, so he should be able to just ignore it when someone does the same back. It's not the first time he's lost his shit when someone has give it back, he's done it on Twitter loads of times too.
I love Carragher, but he's been a fucking idiot here.